Abstract: Supercharacters have recently been proposed as a sort of stand-in for the characters of -groups. If is a prime power, then every set of -powers that contains is both a set of superdegrees and a set of superclass sizes. Moreover, if and are integers that are greater than , then there is an algebra with exactly superdegrees and exactly superclass sizes. These results are direct analogs of results from the theory of -groups.

Gustavo A. Fernández-Alcober and Alexander Moretó, On the Number of Conjugacy Class Sizes and Character Degrees in Finite -groups. Proceedings of the American Mathematical Society 129 (2001), 3201-3204. MR 1844993 (2002d:20009)